fix some quotes

1 files changed, 17 insertions, 17 deletions

diff --git a/essays/admissible_contradictions.tex b/essays/admissible_contradictions.tex
index f66bb98..e95b85f 100644
--- a/essays/admissible_contradictions.tex
+++ b/essays/admissible_contradictions.tex
@@ -15,7 +15,7 @@ could we convey the substance underlying the notations which we call
 admissble contradictions, and motivate the unusual collection of postulates 
 which we will adopt. 
 
-All properties will be thought of as "parameters," such as time, 
+All properties will be thought of as \enquote{parameters,} such as time, 
 location, color, density, acidity, etc. Different parameters will be represented 
 by the letters x, y, z, .... Different values of one parameter, say x, will be 
 represented by $x_1$, $x_2$, .... Each parameter has a domain, the set of all values 
@@ -28,7 +28,7 @@ indefinitely large. By giving a possible phenomenon fixed values for every
 parameter, I assure that there will be only one such possible phenomenon. In 
 other words, my intension sets are all singletons. Another point is that if we 
 specify some of the parameters and specify their ranges, we limit the 
-phenomena which can be represented by our "ensembles." If our first 
+phenomena which can be represented by our \enquote{ensembles.} If our first 
 parameter is time and its range is $R$, and our second parameter is spatial 
 location and its range is $R^2$, then we are limited to phenomena which are 
 point phenomena in space and time. If we have a parameter for speed of 
@@ -41,7 +41,7 @@ Let ($x_1$, $y$, $z$, ...), ($x_2$, $y$, $z$, ...), etc. stand for possible phen
 which all differ from each other in respect to parameter x but are identical in 
 respect to every other parameter $y$, $z$, ... . (If the ensembles were intension 
 sets, they would be disjoint precisely because $x$ takes a different value in 
-each.) A "simple contradiction family" of ensembles is the family [($x_1$,$y$,$z$, 
+each.) A \enquote{simple contradiction family} of ensembles is the family [($x_1$,$y$,$z$, 
 ...), ($x_2$, $y$, $z$, ...), ...]. The family may have any number of ensembles. It 
 actually represents many families, because $y$, $z$, ... are allowed to vary; but 
 each of these parameters must assume the same value in all ensembles in any 
@@ -50,7 +50,7 @@ any one family, values which may be fixed. A parameter which has the same
 value throughout any one family will be referred to as a consistency 
 parameter. A parameter which has a different value in each ensemble in a 
 given family will be referred to as a contradiction parameter. 
-"Contradiction" will be shortened to "con." A simple con family is then a 
+\enquote{Contradiction} will be shortened to \enquote{con.} A simple con family is then a 
 family with one con parameter. The consistency parameters may be dropped 
 from the notation, but the reader must remember that they are implicitly 
 present, and must remember how they function. 
@@ -64,19 +64,19 @@ value from the first subset, one from the second subset, etc.
 
 Con families can be defined which have more than one con parameter, 
 i.e. more than one parameter satisfying all the conditions we put on x. Such 
-con families are not "simple." Let the cardinality of a con family be 
-indicated by a number prefixed to "family," and let the number of con 
-parameters be indicated by a number prefixed to "con." Remembering that 
+con families are not \enquote{simple.} Let the cardinality of a con family be 
+indicated by a number prefixed to \enquote{family,} and let the number of con 
+parameters be indicated by a number prefixed to \enquote{con.} Remembering that 
 consistency parameters are understood, a 2-con $\infty$-family would appear as 
 [($x_1$, $y_1$). ($x_2$, $y_2$), ...].
 
-A "contradiction" or "$\varphi$-object" is not explicitly defined, but it is 
-notated by putting "$\varphi$" in front of a con family. The characteristics of $\varphi$-objects, 
+A \enquote{contradiction} or \enquote{$\varphi$-object} is not explicitly defined, but it is 
+notated by putting \enquote{$\varphi$} in front of a con family. The characteristics of $\varphi$-objects, 
 or cons, are established by introducing additional postulates in the 
 theory. 
 
-In this theory, every con is either "admissible" or "not admissible." 
-"Admissible" will be shortened to "am." The initial amcons of the theory 
+In this theory, every con is either \enquote{admissible} or \enquote{not admissible.} 
+\enquote{Admissible} will be shortened to \enquote{am.} The initial amcons of the theory 
 are introduced by postulate. Essentially, what is postulated is that cons with 
 a certain con parameter are am. (The cons directly postulated to be am are 
 on 1-con families.) However, the postulate will specify other requirements for 
@@ -113,7 +113,7 @@ the literary description of the waterfall illusion!) Note the implicit
 requirements that the con family must be a 2-family, and that $s$ must be 
 selected from $[O]$ in one ensemble and from ${s:s>O}$ in the other ensemble. 
 
-If $t$ is time, $t\in R$, consideration of the phrase "b years ago," which is an 
+If $t$ is time, $t\in R$, consideration of the phrase \enquote{b years ago,} which is an 
 amcon in the natural language, suggests that we postulate $\varphi[(t):a-b\leq t\leq v-b \&a\leq v]$ to be am,
 where $a$ is a fixed time expressed in years A.D., $b$ is a fixed 
 number of years, and $v$ is a variable---the time of the present instant in years 
@@ -133,8 +133,8 @@ obvious. But in this case, there are more requirements in the postulate of
 admissibility. May we apply the postulate twice? May we admit first 
 $\varphi[(p\in P_1),(p\in P_2)]$ and then $\varphi[(p\in P_3),(p\in P_4)]$, where $P_3$ and $P_4$ are arbitrary 
 $P_i$'s different from $P_1$ and $P_2$? The answer is no. We may admit 
-$\varphi[(p\in P_1),(p\in P_2)]$ for arbitrary $P_1$ and $P_2$, $P_1\cap P_2=\emptyset$, but having made this "initial 
-choice," the postulate cannot be reused for arbitrary $P_3$ and $P_4$. A second 
+$\varphi[(p\in P_1),(p\in P_2)]$ for arbitrary $P_1$ and $P_2$, $P_1\cap P_2=\emptyset$, but having made this \enquote{initial 
+choice,} the postulate cannot be reused for arbitrary $P_3$ and $P_4$. A second 
 con $\varphi[(p\in P_3),(p\in P_4)]$, $P_3\cap P_4=\emptyset$, may be postulated to be am only if 
 $P_1\cup P_3$,$P_2\cup P_3$,$P_1\cup P_4$, and $P_2\cup P_4$ are not connected. In other words, you 
 may postulate many cons of the form $\varphi[(p\in P_i),(p\in P_j)]$ to be am, but 
@@ -159,7 +159,7 @@ Our present notation cannot express this result, because it does not
 distinguish between different types of uniform motion throughout a finite 
 region, \ie the types $M$, $C_1$, $C_2$, $D_1$, and $D_2$. Instead, we have infinitesimal 
 motion, which is involved in all the latter types of motion. Questions such as 
-"whether the admissibility of $\varphi[M,S]$ implies the admissibility of $\varphi[C_1,S]$" 
+\enquote{whether the admissibility of $\varphi[M,S]$ implies the admissibility of $\varphi[C_1,S]$} 
 drop out. The reason for the omission in the present theory is our choice of 
 parameters and domains, which we discussed earlier. Our present version is 
 thus not exhaustive. However, the deficiency is not intrinsic to our method; 
@@ -233,8 +233,8 @@ implication was empirically false. The realm of the logically possible is not
 the entire realm of connotative thought; it is just the realm of normal 
 perceptual routines. When the mind is temporarily freed from normal 
 perceptual routines---especially in perceptual illusions, but also in dreams and 
-even in the use of certain "illogical" natural language phrases---it can imagine 
-and visualize the "logically impossible." Every text on perceptual 
+even in the use of certain \enquote{illogical} natural language phrases---it can imagine 
+and visualize the \enquote{logically impossible.} Every text on perceptual 
 psychology mentions this fact, but logicians have never noticed its immense 
 significance. The logically impossible is not a blank; it is a whole layer of 
 meaning and concepts which can be superimposed on conventional logic, but